Hi all, I'm trying to learn how to solve quadratic equations but I've ran into a problem.On the wikipedia page: http://en.wikipedia.org/wiki/Quadratic_equationIt explains the step by step process of solving a quadratic equation using the "Complete the square" method. The fourth step states: "Write the left side as a square, and simplify the right side, if necessary."And this appears to change the expression "x² + 2x + 1" into "(x + 1)²" and I'm not exactly sure how that's come about. Could somebody explain it to me?

Basically,you multiply (x+1) by (x+1). So you goFirst, (x+1)(x+1), which is x*x, or x^2Outside, (x+1)(x+1), which is x*1, or simply xInside, (x+1)(x+1), which is 1*x, or simply xLast, (x+1)(x+1), which is 1*1, or 1Then you put it together and it becomes x^2 + x + x + 1, which is then simplified to x^2 + 2x + 1. This process is called FOIL.

Oh, I didn't read your post closely enough. I don't know the process of getting from "x² + 2x + 1", how I remember solving it in math class is by plugging in random numbers into (ax + b)(cx + d), until it would form the quadratic equation through FOIL. I'm sure there's a better way, I just don't know it.

I'll second what Agro said about the quadratic formula. It's really easy, you just plug in the numbers and out comes the answer. (-b±√(b²-4ac)) / (2a) As far as I remember you use this with a trinomial or something like that... I haven't used it in a while. =P

Thanks for the reply. Yeah, all I remember from secondary school with regards to quadratic equations was that formula. I'm just trying to look at the other methods of solving it to help me get a better understanding. Completing the square is the method that I recall the teacher saying takes too long to work out in an exam. Hurray for the British education system. D: So now I'm trying to learn it on my own and struggling a bit.

Oh, I didn't read your post closely enough. I don't know the process of getting from "x² + 2x + 1", how I remember solving it in math class is by plugging in random numbers into (ax + b)(cx + d), until it would form the quadratic equation through FOIL. I'm sure there's a better way, I just don't know it.

The "plug in numbers" method is bullshit, but all the schools teach it. I don't think that's his question though..."x² + 2x + 1"To be able to simplify, your equation needs to be in the form a^2 + 2ab + b^2 which it already is. Now "a^2 + 2ab + b^2" simplifies into "(a+b)^2", so looking at your equation, the root of x² is x and the root of 1 is 1. Thus you have (x+1)^2.

Oh, I didn't read your post closely enough. I don't know the process of getting from "x² + 2x + 1", how I remember solving it in math class is by plugging in random numbers into (ax + b)(cx + d), until it would form the quadratic equation through FOIL. I'm sure there's a better way, I just don't know it.

The "plug in numbers" method is bullshit, but all the schools teach it. I don't think that's his question though..."x² + 2x + 1"To be able to simplify, your equation needs to be in the form a^2 + 2ab + b^2 which it already is. Now "a^2 + 2ab + b^2" simplifies into "(a+b)^2", so looking at your equation, the root of x² is x and the root of 1 is 1. Thus you have (x+1)^2.

I dot know what your talking about. The quadradic formula is great for getting values of x that aren't whole for polynomials with degrees of two. It doesn't help in factoring at all, but if you already have x, why factor?

Completing the square is the method that I recall the teacher saying takes too long to work out in an exam.

It doesn't take that long, and it's the way that the formula you memorise was derived.

If you're needing to solve quadratic equations for a game, be aware that there are numerical issues with one half of -b +/- sqrt(b^2 - 4ac) when 4ac is small. The way to handle this is to have a case split on the sign of b and then to use the fact that the product of the roots is c/a.

Completing the square is way easier if the variable a in the quadratic equation does not have coefficients, e.g. x2 + 3x + 2. Then it's by far way simpler than having to write out the whole quadratic formula and solve it. But if you have a coefficient for the variable a, it takes way too long.

Completing the square is way easier if the variable a in the quadratic equation does not have coefficients, e.g. x2 + 3x + 2. Then it's by far way simpler than having to write out the whole quadratic formula and solve it. But if you have a coefficient for the variable a, it takes way too long.

Not necessarily true. The multiples of the coefficient of "a" you can plugin on the left of a matrix - and the multiples of "c" you can plug in on the right. For example: 5x2 + 12x + 4----5|2----1|2----Cross multiply and add 5*2 + 2*1 = 12. Which means this is the solution, because it equals the coefficient of x (middle term) - to convert into 2 binomials just do (5x + 2)(x + 2). Obviously, you still have to plug in some numbers, but this way is a lot faster.

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